We introduce Geometric Texton Theory (GTT), a theory of categorical visual feature classification that arises through consideration of the metamerism that affects families of co-localised linear receptive-field operators. A refinement of GTT that uses maximum likelihood (ML) to resolve this metamerism is presented. We describe a method for discovering the ML element of a metamery class by analysing a database of natural images. We apply the method to the simplest case--the ML element of a canonical metamery class defined by co-registering the location and orientation of profiles from images, and affinely scaling their intensities so that they have identical responses to 1-D, zeroth- and first-order, derivative of Gaussian operators. We find that a step edge is the ML profile. This result is consistent with our proposed theory of feature classification.